Question

A function that shifts y=x^2+1 up 5 units

Answer 1

Answer:

$y = {x}^{2} + 6$

Step-by-step explanation:

The given function is

$y = {x}^{2} + 1$

We want to find a function that shifts this function up by 5 units.

We let:

$f(x) = {x}^{2} + 1$

Then the transformed function we are looking for is

$g(x) = f(x) + 5$

This implies that:

$g(x) = {x}^{2} + 1 + 5$

$g(x) = {x}^{2} + 6$

Hence the function we are looking for is

$y = {x}^{2} + 6$